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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm012, 25 pages, doi:10.1093/imrn/rnm012 published on May 24, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Finite Time singularity of the Landau-Lifshitz-Gillbert Equation

Shijin Ding1 and Changyou Wang2,

1 School of Mathematical siences, South China Normal Unoversity, Guangzhou 510631, P. R China
2 Department of mathematics, University of Kentucky, Lexington, KY 40506, USA

Correspondence: Correspondence to be sent to: Changyou Wang, Departent of Mathemtics, University of Kentucky, Lexington, KY 40506, USA. e-mail: cywang{at}ms.uky.edu

We prove that in dimensions three or four, for suitably chosen initial data, the short time smooth solution to the Landau-Lifshitz-Gilbert equation blows up at finite time.

Communicated by Michael Struwe


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